Experimental Comparison of Bohm-like Theories with Different Ontologies

The de Broglie-Bohm theory is a hidden variable interpretation of quantum mechanics which involves particles moving through space with definite trajectories. This theory singles out position as the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum space, and momentum is singled out as the primary ontological variable. In this paper we experimentally show how the two theories lead to different ontological descriptions. We construct the putative particle trajectories for a two-slit experiment in both the position and momentum space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories through the primary and derived (i.e. non-primary) spaces, we compare the ontological pictures offered by the two theories and show that they do not agree. This contradictory behaviour brings into question which ontology for Bohmian mechanics is to be preferred.